Sound-Intensity Probes
The sound-intensity vector is the time average of sound-power flow per unit area expressed in spectral form.
The sound-intensity probe that is currently in greatest use consists of two microphones that measure a single component of the vector along a line joining the microphone centers. Usually the measurement is made in a direction perpendicular to a surface, such as a hypothetical surface enclosing a sound source or the surface of the source itself. Such probes are described in                1. Anon., 1996, “Instruments for Measurement of Sound Intensity”, Standard ANSI S1.9-1996, American National Standards Institute and in        2. F. J. Fahy, 1995, “Sound Intensity”, Second Edition, E& FN Spon, an imprint of Chapman and Hall, London.Sound intensity is generally computed using a mathematical equation involving the cross spectrum of the sound pressures at two microphones. The equation is given in        3. J. Y. Chung, 1980, “Sound Intensity Meter”, U.S. Pat. No. 4,236,040, November 25.It is derived using finite-difference approximations, based on the requirement that the spacing between the microphones is less than the wavelength of sound, divided by 2π. This places an upper limit on the frequency range of the measurement and the microphones must be placed sufficiently close to meet this requirement. There is also a lower limit due to possible error from phase mismatch of the microphones at lower frequencies. This problem is alleviated by placing the microphone further apart. Different microphone spacings are used in practice.        
Recently a new acoustic instrument, the acoustic vector probe (AVP) was developed by                4. R. Hickling 2003, “Acoustic Measurement Method and Apparatus”, patent application to the U.S. Patent and Trademark Office, Ser. No. 10/396,541, Filing Date Mar. 25, 2003.The technical information contained in this application is hereby incorporated herein by reference. An AVP consists of a tetrahedral arrangement of four small microphones that simultaneously measures, at a point, the three fundamental quantities of acoustics, namely the sound-intensity and sound-velocity vectors, and sound pressure. The microphones are arranged in pairs pointing in opposite directions. AVPs are more accurate, more compact and less expensive than previous instruments for measuring the sound-intensity vector.        
The AVP is used principally for locating and quantifying sound sources, as described in                5. R. Hickling, 2003, “Sound Source Location and Quantification using Arrays of Vector Probes”, patent application to the U.S. Patent and Trademark Office, Ser. No. 10/746,763, Filing Date Dec. 26, 2003.The technical information contained in this continuation-in-part is hereby incorporated herein by reference.        
In order for these two types of probe to measure sound intensity accurately, the microphones have to be corrected so that their response is substantially identical over the frequency range of the measurement. This is particularly important for AVPs because, to determine the direction of a sound source accurately, the probe has to be omnidirectional, i. e. with a sensitivity that has no directional bias.
Composite sound-intensity probes having a common coordinate system and measurement point can be constructed, consisting of nested arrangements of either the two-microphone probe or the AVP. These arrangements increase the frequency range of the measurement by extending measurement accuracy for higher and lower frequencies. As before, the microphones in these probes have to have a response that is substantially identical to achieve the required accuracy.
Currently microphones used for sound-intensity measurement are assumed to have a flat response over the frequency range of the measurement. The response is generally depicted on a decibel scale where deviation from flatness appears less significant. Using the flatness assumption, microphones are calibrated and phase-matched at a single frequency, typically about 250 Hz. The calibration and phase-matching are then considered to apply over the appropriate frequency range, as described in Reference 1 and in                6. Anon. 2005, “Notes for Seminar on Sound Intensity”, Published by Bruel and Kjaer, Naerum, Denmark.However on a linear scale the microphones of the sound-intensity probes can be seen to deviate from flatness. Hence calibration and phase-matching at a single frequency cannot be used to make corrections to provide a substantially identical response between microphones. The present invention includes an instrument and a transfer-function method for making such corrections over the frequency range of the measurement. The use of transfer functions is explained in detail in the description of the preferred embodiment.        